1. Field of the Invention
The present invention relates to the design of multi-layer circuits, e.g., integrated circuits or printed circuits, and, more particularly, to determining the electromagnetic effects on the performance of a multi-layer circuit with three-dimensional interconnects from a bias applied to the circuit.
2. Description of Related Art
As the size of electrical devices and interconnecting conductors of multi-layer circuits, especially multi-layer integrated circuits, continues to decrease and the bandwidth of operation continues to increase, the effects on the performance of the circuit due to electromagnetic effects in the various layers of the circuit have become more pronounced.
According to some conventional approaches, analysis of these effects on each circuit layer has been limited to evaluating such effect due to current flowing only in the layer itself. See for example, “An Efficient Algorithm For Analyzing Large-Scale Microstrip Structures Using Adaptive Integral Method Combined With Discrete Complex-Image Method”, by Ling et al., IEEE Transactions On Microwave Theory And Techniques, Vol. 48, No. 5, pp. 832-839, (May 2000); “AIM: Adaptive Integral Method For Solving Large-Scale Electromagnetic Scattering And Radiation Problems”, by Bleszynski et al., Radio Science, Volume 31, Number 5, Pages 1225-1251, (September-October 1996); and “A Precorrected-FFT Method For Electrostatic Analysis Of Complicated 3-D Structures”, by Phillips et al., IEEE Transactions On Computer-Aided Design Of Integrated Circuits And Systems, Vol. 16, No. 10, pp. 1059-1072, (October 1997).
While this approach has been applied successfully in the past, the increasing density of devices and the reduction in size of interconnecting conductors in the design of multi-layer circuits has required that the effects on the performance of the circuit due to the cumulative effects of currents flowing in all of the layers of the circuit be considered. Furthermore, the development of nanometer-scale technologies has enabled denser integration of functional components in silicon substrates and led to more stringent requirements for design verification. As a result, conventional modeling of the layers has become inadequate and more accurate three-dimensional modeling of the electromagnetic effects will be needed for future applications.
Thus, there is a need for improved methods and related tools for electromagnetic modeling of multi-layer circuits.